Correct option is (B) \(3 \sqrt{2}\)
The given points are \(A(1,-3)\) and \(B(4,-6)\)
Then, \(\left(x_{1}=1, y_{1}=-3\right)\) and \(\left(x_{2}=4, y_{2}=-6\right)\)
\(A B =\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\)
\(=\sqrt{(4-1)^{2}+(-6-(-3))^{2}} \)
\(=\sqrt{(3)^{2}+(-6+3)^{2}} \)
\(=\sqrt{9+(-3)^{2}} \)
\( =\sqrt{9+9}\)
\(=\sqrt{18}\)
\(=3 \sqrt{2}\) units
